TY - JOUR

T1 - Levitation of evaporating microscale droplets over solid surfaces

AU - Ajaev, Vladimir S.

AU - Zaitsev, Dmitry V.

AU - Kabov, Oleg A.

N1 - Funding Information: The work was supported by the Russian Science Foundation (Grant No.18-19-00538). We thank D. P. Kirichenko for valuable discussions and for sharing experimental data with us. Publisher Copyright: © 2021 American Physical Society.

PY - 2021/5

Y1 - 2021/5

N2 - We develop an analytical model to describe recent experimental observations of levitation of evaporating microscale droplets over heated solid surfaces at temperatures far below the Leidenfrost point. Viscous flow patterns around the droplet are determined from the solution of the equation for the Stokes stream function in bipolar coordinates. The results are compared to the predictions of models representing microscale droplets as point sources in the Stokes flow equations. Formulas for the force acting on the droplet as a result of moist air flow around it are derived and used to obtain predictions of levitation height as a function of droplet size which are in very good agreement with the experimental data. In addition to gravity, three physical mechanisms are identified which contribute to the force acting on the droplet: repulsive interaction of the droplet with the solid, spatially nonuniform evaporation along the liquid surface, and thermocapillary effect. The first two act against gravity and allow droplets to levitate despite competing thermocapillary stresses which push the moist air out of the region between the droplet and the solid. Relative importance of the three mechanisms is evaluated based on an analytical model of heat transfer both inside and outside of the droplet.

AB - We develop an analytical model to describe recent experimental observations of levitation of evaporating microscale droplets over heated solid surfaces at temperatures far below the Leidenfrost point. Viscous flow patterns around the droplet are determined from the solution of the equation for the Stokes stream function in bipolar coordinates. The results are compared to the predictions of models representing microscale droplets as point sources in the Stokes flow equations. Formulas for the force acting on the droplet as a result of moist air flow around it are derived and used to obtain predictions of levitation height as a function of droplet size which are in very good agreement with the experimental data. In addition to gravity, three physical mechanisms are identified which contribute to the force acting on the droplet: repulsive interaction of the droplet with the solid, spatially nonuniform evaporation along the liquid surface, and thermocapillary effect. The first two act against gravity and allow droplets to levitate despite competing thermocapillary stresses which push the moist air out of the region between the droplet and the solid. Relative importance of the three mechanisms is evaluated based on an analytical model of heat transfer both inside and outside of the droplet.

UR - http://www.scopus.com/inward/record.url?scp=85107301860&partnerID=8YFLogxK

U2 - 10.1103/PhysRevFluids.6.053602

DO - 10.1103/PhysRevFluids.6.053602

M3 - Article

AN - SCOPUS:85107301860

VL - 6

JO - Physical Review Fluids

JF - Physical Review Fluids

SN - 2469-990X

IS - 5

M1 - 053602

ER -